This application claims the priorities of Japanese Patent Application No. 2000-397246 filed on Dec. 27, 2000 and Japanese Patent Application No. 2001-354545 filed on Nov. 20, 2001, which are incorporated herein by reference.
1. Field of the Invention
The present invention relates to a method of detecting a posture of an object by which an inclination of the object is detected, and an apparatus using the same. In particular, the present invention relates to a method of detecting a posture of an object by which the posture (inclination) of the object is automatically detected when the object (or a reference) is shifted by use of an actuator in an automatic stage or automatic measuring device such as an interferometer, and an apparatus using the same.
2. Description of the Prior Art
As an apparatus for detecting a posture (pitching, rolling, or the similar) of a moving object, an autocollimator such as the one shown in FIG. 10 has conventionally been known. This autocollimator is one which irradiates an object 203 with a laser luminous flux by way of a PBS 201 and a quarter-wave plate 202; illuminates a PSD (Position Sensitive Device) 205, which is an analog position sensor, with the luminous flux reflected by the object 203 by way of the quarter-wave plate 202, the PBS 201, and a lens 204; and determines the posture (inclination a) of the object 203 according to the distance d from the center axis of the PSD 205 to the position irradiated with the luminous flux. The inclination a in this case is determined by use of the expression of d=fxc2x7tan 2xcex1 (where f is the focal length of the lens 204).
Since the detection accuracy of the autocollimator is proportional to the focal length f of the lens 204 as can be seen from the above-mentioned expression, the focal length f increases when the detection accuracy is to be raised, whereby the apparatus becomes larger.
Therefore, in order to enable highly accurate detection while preventing the apparatus from becoming larger, a technique has been known in which, as shown in FIG. 11 for example, two interference displacement meters 211, 212 are installed in parallel in an object 210, the difference between the respective distances d1, d2 from the interference displacement meters 211, 212 to a straightedge 214 arranged perpendicular to a reference table 213 is determined, and the posture (rolling angle) of the object 210 is calculated from this difference. Specifically, the rolling angle is expressed by:
xcex1=tanxe2x88x921[(d1xe2x88x92d2)/D]
where D is the distance between the two interference displacement meters 211, 212.
In such a technique, however, it is necessary for the interference displacement meters 211, 212 to be attached directly to the object. Since this technique fails to provide a so-called non-contact type, various problems occur, and it is also problematic in that the configuration of the apparatus becomes too complicated. In particular, at least three interference displacement meters are necessary in the two-dimensional posture detection, whereby their mutual alignment adjustment becomes complicated. Further, it is necessary to detect the above-mentioned distance D precisely, which makes the system hard to adjust.
In order to overcome the problems mentioned above, it is an objective of the present invention to provide a method of detecting a posture of an object by which the posture of the object, such as a two-dimensional posture in particular, can be obtained by a highly-accurate, high-speed, non-contact, and simple system configuration, and an apparatus using the same.
The present invention provides a method of detecting a posture of an object, by which a relative inclination of the object with respect to a reference is detected, the method comprising the steps of:
acquiring fringe image data carrying phase information of the object;
subjecting the whole or part of the fringe image data to arithmetic processing using Fourier transform so as to determine a tilt frequency of a fringe corresponding to an inclination of the object in the fringe image data; and
detecting the inclination of the object according to the tilt frequency.
The tilt frequency may be determined by defining positional coordinates of a predetermined peak in peaks on a frequency coordinate system obtained by the Fourier transform and carrying out an arithmetic operation for calculating the tilt frequency according to the positional coordinates.
The present invention provides an apparatus for detecting a posture of an object, which detects phase information from the object and a relative inclination of the object with respect to a reference, the apparatus comprising:
fringe image data acquiring means for acquiring fringe image data carrying the phase information from the object;
Fourier transform arithmetic means for subjecting the whole or part of the fringe image data to arithmetic processing using Fourier transform;
tilt frequency calculation means for determining a tilt frequency of a fringe corresponding to an inclination of the object in the fringe image data; and
object inclination detection means for detecting an inclination of the object according to the tilt frequency.
The present invention provides a method of detecting a posture of an object, by which a relative inclination of the object with respect to a reference is detected, the method comprising the steps of:
acquiring fringe image data carrying phase information of the object;
subjecting the whole or part of the fringe image data to arithmetic processing using Fourier transform so as to determine phase information including an inclination of the object; and
subjecting thus obtained phase information of the object to a predetermined arithmetic operation so as to detect the inclination of the object.
The phase information of the object may be determined by defining a predetermined spectrum distribution of a fringe corresponding to the inclination of the object in spectrum distributions on a frequency coordinate system obtained by the Fourier transform and carrying out an arithmetic operation for calculating the phase information according to the predetermined spectrum distribution.
Preferably, the predetermined arithmetic operation is an arithmetic operation for determining a least-square plane fitting the phase information of the object.
The present invention provides an apparatus for detecting a posture of an object, which detects phase information from the object and a relative inclination of the object with respect to a reference, the apparatus comprising:
fringe image data acquiring means for acquiring fringe image data carrying phase information from the object;
Fourier transform arithmetic means for subjecting the whole or part of the fringe image data to arithmetic processing using Fourier transform;
object phase information calculation means for determining phase information including an inclination of the object according to the fringe image data subjected to the Fourier transform; and
object inclination detection means for detecting the inclination of the object according to the phase information of the object.
The method and apparatus for detecting a posture of an object in accordance with the present invention are particularly effective when the object or a reference body providing a reference for the inclination of the object is a moving member movable by an actuator. The actuator may be a piezoelectric device.
The present invention provides a method of detecting a posture of an object, by which a change in inclination of the object between before and after a movement thereof is detected, the method comprising:
a first step of acquiring first fringe image data carrying phase information of the object before the movement,
subjecting the whole or part of the first fringe image data to arithmetic processing using Fourier transform so as to determine a tilt frequency of a fringe corresponding to an inclination of the object before the movement in the first fringe image data, and
detecting inclination information of the object before the movement according to the tilt frequency;
a second step of acquiring second fringe image data carrying phase information of the object after the movement,
subjecting the whole or part of the second fringe image data to arithmetic processing using Fourier transform so as to determine a tilt frequency of a fringe corresponding to an inclination of the object after the movement in the second fringe image data, and
detecting inclination information of the object after the movement according to the tilt frequency; and
a third step of determining a difference in inclination information of the object between before and after the movement detected by the first and second steps, and detecting a change in inclination of the object between before and after the movement.
The present invention provides a method of detecting a posture of an object, by which a change in inclination of the object between before and after a movement is detected, the method comprising:
a first step of acquiring first fringe image data carrying phase information of the object before the movement, and
subjecting the whole or part of the first fringe image data to arithmetic processing using Fourier transform so as to determine a tilt frequency of a fringe corresponding to an inclination of the object before the movement in the first fringe image data;
a second step of acquiring second fringe image data carrying phase information of the object after the movement, and
subjecting the whole or part of the second fringe image data to arithmetic processing using Fourier transform so as to determine a tilt frequency of a fringe corresponding to an inclination of the object after the movement in the second fringe image data; and
a third step of determining a difference between the tilt frequencies of the fringes corresponding to the inclinations of the object before and after the movement determined by the first and second steps, and detecting a change in inclination of the object between before and after the movement according to thus determined difference.
In the method or apparatus for detecting a posture of an object in accordance with the present invention, the phase information may be interference fringe information.
In the present invention, the apparatus may be a Michelson type interferometer. The object may have a rough surface.
In the present invention, the relative inclination of the object with respect to a reference refers to a relative angle between the reference (e.g., a horizontal plane, a reference surface in an interferometer, etc.) for determining an inclination and a surface (posture reference surface) acting as a reference for detecting the posture of the object. As the posture reference surface of the object, a face (surface) whose form is to be measured in a lightwave interferometer, a surface of the object coming into contact with a mounting table, and the like, for example, can be set when appropriate.
As for the background art of the present invention, the disclosure in the following publication has been known, for example:
M. Takeda, H. Ina and S. Kobayashi: Fourier transforms method of fringe-pattern analysis for computer-based topography and interferometry, J. Opt. Soc. Am. 72 (1982), p. 156.
The above-mentioned publication discloses that a plurality of Fourier spectrum peaks including a peak corresponding to a carrier fringe can be obtained when the carrier fringe is superposed on a fringe image and then the resulting data is subjected to Fourier transform. This is basically different in terms of the idea and purpose from the present invention, which takes account of meanings of individual peaks and spectrum distributions of a Fourier spectrum and detects a posture of an object according to a predetermined isolated peak or spectrum distribution.
Namely, the Fourier transform fringe analysis method disclosed in the above-mentioned publication artificially provides a relative inclination between an object and a reference in order to analyze phase information inherent in the object such as a surface form thereof, thereby superposing a carrier fringe onto a fringe image. On a frequency space obtained upon the Fourier transform, the information of the artificially superposed carrier fringe is isolated, as a frequency (carrier frequency) corresponding to the carrier fringe, from the phase information inherent in the object.
By contrast, without artificially superposing the carrier fringe, the present invention captures the inclination of the object inclined beforehand as phase information inherent in the object. When the phase information including the inclination is subjected to Fourier transform, the frequency corresponding to the inclination of the object on a frequency space can be isolated as with the artificially superposed carrier frequency mentioned above.
In the present specification, the frequency on a frequency space corresponding to the inclination of the object will be referred to as xe2x80x9ctilt frequencyxe2x80x9d so as to clarify that it is different from the artificially superposed carrier frequency.